关键词: 单纯形, 高斯积分, 有限元, 代数精度, 积分余项

Abstract: Based on the remainder term of Gauss-Legendre quadrature rule, the corresponding correction quadrature formulas, which increase the algebraic accuracy at least two-order, are proposed. Using the coordinate transformation to change the integral over the triangle and tetrahedral into an equivalent integral over the square and cube, the correction formula of Gaussian quadrature rule is extended to calculate the multiple integral over a multi-dimensional simplex. Compared with Hammer quadrature formulae over two-dimensional triangular elements and three-dimensional tetrahedral elements, it is shown that the corrected quadrature formula is of high accuracy, can quickly converge to the exact value of the integral. Thus it is of great use in many engineering applications.

Key words: simplex, Gauss quadrature, finite element, algebraic accuracy, integral remainder